краевые задачи

The Second Boundary Problem for the System Hyperbolic Type Second Order for Large T

Authors: Lexina S. V.

In the paper we consider the control problem for objects which vibration are described by the system of ware equations with boundary condition of the second kind.

Boundary Properties of Generalized Cauchy Type Integrals in the Space of Smooth Functions

Authors: Soldatova T. A.

The generalized Cauchy type integrals which kernel depends on the difference of arguments are considered on the smooth contour. These integrals cover as potentials of double layer for second order elliptic equations as generalized Cauchy type integrals for first order elliptic systems on the plane. In the paper the sufficient conditions such that these integrals belong C n,μ up to the boundary are found.

Finite Integral Transformations Method — Generalization of Classic Procedure for Eigenvector Decomposition

Authors: Senitsky Y. E.

The structural algorithm of the finite integral transformation method is presented as a generalization of the classical procedure of eigenvector decomposition. The initial-boundary problems described with a hyperbolic system of linear partial second order differential equations are considered. The general case of non-self adjoint solution by expansion in the vector-functions is possible only by the use of biorthogonal of finite integral transformations.

About Completeness of Products of Functions, Initiated by Singular Differential Equations

Authors: Poplavskij D. V.

In this article we introduced the completeness theorem for special vector-functions, initiated by products of Weil solutions of forth order differential equation and its derivatives on the halfline. We prove that such nonlinear combinations of Weil solutions and its derivatives form the linear subspace of solutions, which decrease to infinity, of linear singular Kamke-type differential system.

О решениях некоторых краевых задач для общего уравнения КдФ

Authors: Ignatyev M. Y.

В работе рассматривается общее уравнение иерархии Кортевега-де Фриза (КдФ). Изучаются краевые задачи для данного уравнения с неоднородными граничными условиями специального вида. Построен широкий класс решений изучаемых задач. Построение основано на идеях метода обратной спектральной задачи.